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Some investigation on Hermitian positive definite solutions of the matrix equation

✍ Scribed by Jing Cai; Guoliang Chen

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
162 KB
Volume
430
Category
Article
ISSN
0024-3795

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✦ Synopsis

In this paper, the Hermitian positive definite solutions of the matrix equation X s + A * X -t A = Q are considered, where Q is an Hermitian positive definite matrix, s and t are positive integers. Necessary and sufficient conditions for the existence of an Hermitian positive definite solution are derived. A sufficient condition for the equation to have only two different Hermitian positive definite solutions and the formulas for these solutions are obtained. In particular, the equation with the case AQ

A necessary condition for the existence of an Hermitian positive definite solution and some new properties of the Hermitian positive definite solutions are given, which generalize the existing related results.

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In this paper we investigate nonlinear matrix equations X Β± A \* X -q A = Q where q β‰₯ 1. We derive necessary conditions and sufficient conditions for the existence of positive definite solutions for these equations. We provide a sufficient condition for the equation X + A \* X -q A = Q to have two